{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4VZ56Q3GITPJX45YIRTUPVRUYC","short_pith_number":"pith:4VZ56Q3G","canonical_record":{"source":{"id":"1701.06139","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-22T08:43:48Z","cross_cats_sorted":[],"title_canon_sha256":"56e7ff839e5e69add9d708e72ab182a9e7fab53989b90e7732736d79cf79f3cd","abstract_canon_sha256":"428f1c5f099edc7ca86eacfeeae012269c9e97c65c1c78c3b429e50e475d5c02"},"schema_version":"1.0"},"canonical_sha256":"e573df436644de9bf3b8446747d634c090fe31e7e8022f92031a16c18a3f21ec","source":{"kind":"arxiv","id":"1701.06139","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06139","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06139v1","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06139","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"pith_short_12","alias_value":"4VZ56Q3GITPJ","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4VZ56Q3GITPJX45Y","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4VZ56Q3G","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4VZ56Q3GITPJX45YIRTUPVRUYC","target":"record","payload":{"canonical_record":{"source":{"id":"1701.06139","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-22T08:43:48Z","cross_cats_sorted":[],"title_canon_sha256":"56e7ff839e5e69add9d708e72ab182a9e7fab53989b90e7732736d79cf79f3cd","abstract_canon_sha256":"428f1c5f099edc7ca86eacfeeae012269c9e97c65c1c78c3b429e50e475d5c02"},"schema_version":"1.0"},"canonical_sha256":"e573df436644de9bf3b8446747d634c090fe31e7e8022f92031a16c18a3f21ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:19.179002Z","signature_b64":"LmyA+5wKDzTkLDSzysJ5IbXMIzy35GDEH2kcTotvEQc4FSom4B7EndHUN9Kuh53Mbf5l3aYie4OMU+WUnl07BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e573df436644de9bf3b8446747d634c090fe31e7e8022f92031a16c18a3f21ec","last_reissued_at":"2026-05-18T00:52:19.178562Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:19.178562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.06139","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2cEjGNM4HGuwKW9SQxdGv21Xc7M+52qewiCbYHpBGanhpX2o0Nr4vTpF4BKjFJpGL7mj6tgO8wOtp1bRhJqLBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T00:29:51.563051Z"},"content_sha256":"3b0881f4b3a823f7ce9b1dfb823ff52e1ba2eabbbee90f06a62db024ea5b6c89","schema_version":"1.0","event_id":"sha256:3b0881f4b3a823f7ce9b1dfb823ff52e1ba2eabbbee90f06a62db024ea5b6c89"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4VZ56Q3GITPJX45YIRTUPVRUYC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dense $3$-uniform hypergraphs containing a large clique","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Biao Wu, Yuejian Peng","submitted_at":"2017-01-22T08:43:48Z","abstract_excerpt":"An $r$-uniform graph $G$ is dense if and only if every proper subgraph $G'$ of $G$ satisfies $\\lambda (G') < \\lambda (G)$, where $\\lambda (G)$ is the Lagrangian of a hypergraph $G$. In 1980's, Sidorenko showed that $\\pi(F)$, the Tur\\'an density of an $r$-uniform hypergraph $F$ is $r!$ multiplying the supremum of the Lagrangians of all dense $F$-hom-free $r$-uniform hypergraphs. This connection has been applied in estimating Tur\\'an density of hypergraphs. When $r=2$, the result of Motzkin and Straus shows that a graph is dense if and only if it is a complete graph. However, when $r\\ge 3$, it b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06139","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9YR8cU8dVcMFpuVeRVNphiDN5CuoepOT5qFu3DRP671A1dlElANnvip1Z/PXjg0zZ8uTpmVVuECx6kPe6UK7Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T00:29:51.563408Z"},"content_sha256":"34cea5d709823ef9da81d7513c6b3f19ba1e573eabca06a3601f14b75483aa41","schema_version":"1.0","event_id":"sha256:34cea5d709823ef9da81d7513c6b3f19ba1e573eabca06a3601f14b75483aa41"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4VZ56Q3GITPJX45YIRTUPVRUYC/bundle.json","state_url":"https://pith.science/pith/4VZ56Q3GITPJX45YIRTUPVRUYC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4VZ56Q3GITPJX45YIRTUPVRUYC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T00:29:51Z","links":{"resolver":"https://pith.science/pith/4VZ56Q3GITPJX45YIRTUPVRUYC","bundle":"https://pith.science/pith/4VZ56Q3GITPJX45YIRTUPVRUYC/bundle.json","state":"https://pith.science/pith/4VZ56Q3GITPJX45YIRTUPVRUYC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4VZ56Q3GITPJX45YIRTUPVRUYC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4VZ56Q3GITPJX45YIRTUPVRUYC","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"428f1c5f099edc7ca86eacfeeae012269c9e97c65c1c78c3b429e50e475d5c02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-22T08:43:48Z","title_canon_sha256":"56e7ff839e5e69add9d708e72ab182a9e7fab53989b90e7732736d79cf79f3cd"},"schema_version":"1.0","source":{"id":"1701.06139","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06139","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06139v1","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06139","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"pith_short_12","alias_value":"4VZ56Q3GITPJ","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4VZ56Q3GITPJX45Y","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4VZ56Q3G","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:34cea5d709823ef9da81d7513c6b3f19ba1e573eabca06a3601f14b75483aa41","target":"graph","created_at":"2026-05-18T00:52:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"An $r$-uniform graph $G$ is dense if and only if every proper subgraph $G'$ of $G$ satisfies $\\lambda (G') < \\lambda (G)$, where $\\lambda (G)$ is the Lagrangian of a hypergraph $G$. In 1980's, Sidorenko showed that $\\pi(F)$, the Tur\\'an density of an $r$-uniform hypergraph $F$ is $r!$ multiplying the supremum of the Lagrangians of all dense $F$-hom-free $r$-uniform hypergraphs. This connection has been applied in estimating Tur\\'an density of hypergraphs. When $r=2$, the result of Motzkin and Straus shows that a graph is dense if and only if it is a complete graph. However, when $r\\ge 3$, it b","authors_text":"Biao Wu, Yuejian Peng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-22T08:43:48Z","title":"Dense $3$-uniform hypergraphs containing a large clique"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06139","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3b0881f4b3a823f7ce9b1dfb823ff52e1ba2eabbbee90f06a62db024ea5b6c89","target":"record","created_at":"2026-05-18T00:52:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"428f1c5f099edc7ca86eacfeeae012269c9e97c65c1c78c3b429e50e475d5c02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-22T08:43:48Z","title_canon_sha256":"56e7ff839e5e69add9d708e72ab182a9e7fab53989b90e7732736d79cf79f3cd"},"schema_version":"1.0","source":{"id":"1701.06139","kind":"arxiv","version":1}},"canonical_sha256":"e573df436644de9bf3b8446747d634c090fe31e7e8022f92031a16c18a3f21ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e573df436644de9bf3b8446747d634c090fe31e7e8022f92031a16c18a3f21ec","first_computed_at":"2026-05-18T00:52:19.178562Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:19.178562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LmyA+5wKDzTkLDSzysJ5IbXMIzy35GDEH2kcTotvEQc4FSom4B7EndHUN9Kuh53Mbf5l3aYie4OMU+WUnl07BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:19.179002Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.06139","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b0881f4b3a823f7ce9b1dfb823ff52e1ba2eabbbee90f06a62db024ea5b6c89","sha256:34cea5d709823ef9da81d7513c6b3f19ba1e573eabca06a3601f14b75483aa41"],"state_sha256":"eabfeee476fc5c8460ab7ba2a6dda716509831e9ae8a625626263cddf7e78341"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aSaI3Z+pAjRINbamcYURXbGexn6WcoTHHAJh1ZH5BZFl1A4vPYSklmhAkeHtBm97jaQuJXtw+d+POT0Ex9hZBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T00:29:51.565244Z","bundle_sha256":"22ccb958920490e1b820cfc9d647f156216d14a901af17775964a1b2c5bfae36"}}